A Comparison of Atomistic and Surface Enhanced Continuum Approaches at Finite Temperature
The surface of a continuum body generally exhibits properties that differ from those of the bulk. Surface effects can play a significant role for nanomaterials, in particular, due to their large value of surface-to-volume ratio. The effect of solid surfaces at the nanoscale is generally investigated using either atomistic or enhanced continuum models based on surface elasticity theory. Hereby the surface is equipped with its own constitutive structure. Atomistic simulations provide detailed information on the response of the material. Discrete and continuum systems are linked using averaging procedures which allow continuum quantities such as stress to be obtained from atomistic calculations. The objective of this contribution is to compare the numerical approximations of the surface elasticity theory to a molecular dynamics based atomistic model at finite temperature. The bulk thermo-elastic parameters for the continuum’s constitutive model are obtained from the atomistic simulation. The continuum model takes as its basis the fully nonlinear thermo-elasticity theory and is implemented using the finite element method. A representative numerical simulation of face-centered cubic copper confirms the ability of a surface enhanced continuum formulation to reproduce the behaviour exhibited by the atomistic model, but at a far reduced computational cost.
KeywordsRepresentative Volume Element Deformation Gradient Atomistic Simulation Reference Configuration Continuum Field
The first author is grateful to the German Science Foundation (Deutsche Forschungs-Gemeinschaft), grant STE 544/46-1, for their financial support. The support of this work by the ERC Advanced Grant MOCOPOLY is gratefully acknowledged by the second and third authors.
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